TSTP Solution File: NUN081+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUN081+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:10:32 EDT 2022
% Result : Theorem 1.63s 1.85s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 6 RR)
% Number of literals : 22 ( 7 equ; 9 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 19 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r1(A)
| A = dollar_c1 ),
file('NUN081+2.p',unknown),
[] ).
cnf(2,axiom,
( A != dollar_c1
| r1(A) ),
file('NUN081+2.p',unknown),
[] ).
cnf(4,axiom,
( A != dollar_f1(B)
| r2(B,A) ),
file('NUN081+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ r3(A,B,C)
| C != D
| ~ r2(E,D)
| ~ r2(F,E)
| ~ r1(G)
| ~ r2(G,F) ),
file('NUN081+2.p',unknown),
[] ).
cnf(17,axiom,
A = A,
file('NUN081+2.p',unknown),
[] ).
cnf(32,axiom,
r1(dollar_f12(A)),
file('NUN081+2.p',unknown),
[] ).
cnf(33,axiom,
r3(A,dollar_f12(A),dollar_f13(A)),
file('NUN081+2.p',unknown),
[] ).
cnf(35,axiom,
dollar_f13(A) = A,
file('NUN081+2.p',unknown),
[] ).
cnf(49,plain,
r3(A,dollar_f12(A),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[33]),35]),
[iquote('back_demod,33,demod,35')] ).
cnf(53,plain,
r2(A,dollar_f1(A)),
inference(hyper,[status(thm)],[17,4]),
[iquote('hyper,17,4')] ).
cnf(54,plain,
r1(dollar_c1),
inference(hyper,[status(thm)],[17,2]),
[iquote('hyper,17,2')] ).
cnf(60,plain,
dollar_f12(A) = dollar_c1,
inference(hyper,[status(thm)],[32,1]),
[iquote('hyper,32,1')] ).
cnf(61,plain,
r3(A,dollar_c1,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),60]),
[iquote('back_demod,49,demod,60')] ).
cnf(87,plain,
$false,
inference(hyper,[status(thm)],[61,11,35,53,53,54,53]),
[iquote('hyper,61,11,34,53,53,54,53')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN081+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 02:41:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.63/1.85 ----- Otter 3.3f, August 2004 -----
% 1.63/1.85 The process was started by sandbox on n024.cluster.edu,
% 1.63/1.85 Wed Jul 27 02:41:25 2022
% 1.63/1.85 The command was "./otter". The process ID is 9205.
% 1.63/1.85
% 1.63/1.85 set(prolog_style_variables).
% 1.63/1.85 set(auto).
% 1.63/1.85 dependent: set(auto1).
% 1.63/1.85 dependent: set(process_input).
% 1.63/1.85 dependent: clear(print_kept).
% 1.63/1.85 dependent: clear(print_new_demod).
% 1.63/1.85 dependent: clear(print_back_demod).
% 1.63/1.85 dependent: clear(print_back_sub).
% 1.63/1.85 dependent: set(control_memory).
% 1.63/1.85 dependent: assign(max_mem, 12000).
% 1.63/1.85 dependent: assign(pick_given_ratio, 4).
% 1.63/1.85 dependent: assign(stats_level, 1).
% 1.63/1.85 dependent: assign(max_seconds, 10800).
% 1.63/1.85 clear(print_given).
% 1.63/1.85
% 1.63/1.85 formula_list(usable).
% 1.63/1.85 all A (A=A).
% 1.63/1.85 exists Y24 all X19 (-r1(X19)&X19!=Y24|r1(X19)&X19=Y24).
% 1.63/1.85 all X11 exists Y21 all X12 (-r2(X11,X12)&X12!=Y21|r2(X11,X12)&X12=Y21).
% 1.63/1.85 all X13 X14 exists Y22 all X15 (-r3(X13,X14,X15)&X15!=Y22|r3(X13,X14,X15)&X15=Y22).
% 1.63/1.85 all X16 X17 exists Y23 all X18 (-r4(X16,X17,X18)&X18!=Y23|r4(X16,X17,X18)&X18=Y23).
% 1.63/1.85 all X1 X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15)&r3(X1,Y15,Y5)))&Y5=Y4))& (exists Y7 (r2(Y7,Y4)&r3(X1,X8,Y7)))).
% 1.63/1.85 all X2 X9 exists Y2 ((exists Y3 ((exists Y14 (r2(X9,Y14)&r4(X2,Y14,Y3)))&Y3=Y2))& (exists Y6 (r3(Y6,X2,Y2)&r4(X2,X9,Y6)))).
% 1.63/1.85 all X3 X10 ((all Y12 ((all Y13 (-r2(X3,Y13)|Y13!=Y12))| -r2(X10,Y12)))|X3=X10).
% 1.63/1.85 all X4 exists Y9 ((exists Y16 (r1(Y16)&r3(X4,Y16,Y9)))&Y9=X4).
% 1.63/1.85 all X5 exists Y8 ((exists Y17 (r1(Y17)&r4(X5,Y17,Y8)))& (exists Y18 (r1(Y18)&Y8=Y18))).
% 1.63/1.85 all X6 ((exists Y19 (r1(Y19)&X6=Y19))| (exists Y1 Y11 (r2(Y1,Y11)&X6=Y11))).
% 1.63/1.85 all X7 Y10 ((all Y20 (-r1(Y20)|Y20!=Y10))| -r2(X7,Y10)).
% 1.63/1.85 -(exists Y1 Y2 Y3 (r3(Y1,Y2,Y3)& (exists Y4 (Y3=Y4& (exists Y5 (r2(Y5,Y4)& (exists Y6 (r2(Y6,Y5)& (exists Y7 (r1(Y7)&r2(Y7,Y6))))))))))).
% 1.63/1.85 end_of_list.
% 1.63/1.85
% 1.63/1.85 -------> usable clausifies to:
% 1.63/1.85
% 1.63/1.85 list(usable).
% 1.63/1.85 0 [] A=A.
% 1.63/1.85 0 [] -r1(X19)|X19=$c1.
% 1.63/1.85 0 [] X19!=$c1|r1(X19).
% 1.63/1.85 0 [] -r2(X11,X12)|X12=$f1(X11).
% 1.63/1.85 0 [] X12!=$f1(X11)|r2(X11,X12).
% 1.63/1.85 0 [] -r3(X13,X14,X15)|X15=$f2(X13,X14).
% 1.63/1.85 0 [] X15!=$f2(X13,X14)|r3(X13,X14,X15).
% 1.63/1.85 0 [] -r4(X16,X17,X18)|X18=$f3(X16,X17).
% 1.63/1.85 0 [] X18!=$f3(X16,X17)|r4(X16,X17,X18).
% 1.63/1.85 0 [] r2(X8,$f4(X1,X8)).
% 1.63/1.85 0 [] r3(X1,$f4(X1,X8),$f5(X1,X8)).
% 1.63/1.85 0 [] $f5(X1,X8)=$f7(X1,X8).
% 1.63/1.85 0 [] r2($f6(X1,X8),$f7(X1,X8)).
% 1.63/1.85 0 [] r3(X1,X8,$f6(X1,X8)).
% 1.63/1.85 0 [] r2(X9,$f8(X2,X9)).
% 1.63/1.85 0 [] r4(X2,$f8(X2,X9),$f9(X2,X9)).
% 1.63/1.85 0 [] $f9(X2,X9)=$f11(X2,X9).
% 1.63/1.85 0 [] r3($f10(X2,X9),X2,$f11(X2,X9)).
% 1.63/1.85 0 [] r4(X2,X9,$f10(X2,X9)).
% 1.63/1.85 0 [] -r2(X3,Y13)|Y13!=Y12| -r2(X10,Y12)|X3=X10.
% 1.63/1.85 0 [] r1($f12(X4)).
% 1.63/1.85 0 [] r3(X4,$f12(X4),$f13(X4)).
% 1.63/1.85 0 [] $f13(X4)=X4.
% 1.63/1.85 0 [] r1($f14(X5)).
% 1.63/1.85 0 [] r4(X5,$f14(X5),$f16(X5)).
% 1.63/1.85 0 [] r1($f15(X5)).
% 1.63/1.85 0 [] $f16(X5)=$f15(X5).
% 1.63/1.85 0 [] r1($f17(X6))|r2($f19(X6),$f18(X6)).
% 1.63/1.85 0 [] r1($f17(X6))|X6=$f18(X6).
% 1.63/1.85 0 [] X6=$f17(X6)|r2($f19(X6),$f18(X6)).
% 1.63/1.85 0 [] X6=$f17(X6)|X6=$f18(X6).
% 1.63/1.85 0 [] -r1(Y20)|Y20!=Y10| -r2(X7,Y10).
% 1.63/1.85 0 [] -r3(Y1,Y2,Y3)|Y3!=Y4| -r2(Y5,Y4)| -r2(Y6,Y5)| -r1(Y7)| -r2(Y7,Y6).
% 1.63/1.85 end_of_list.
% 1.63/1.85
% 1.63/1.85 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.63/1.85
% 1.63/1.85 This ia a non-Horn set with equality. The strategy will be
% 1.63/1.85 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.63/1.85 deletion, with positive clauses in sos and nonpositive
% 1.63/1.85 clauses in usable.
% 1.63/1.85
% 1.63/1.85 dependent: set(knuth_bendix).
% 1.63/1.85 dependent: set(anl_eq).
% 1.63/1.85 dependent: set(para_from).
% 1.63/1.85 dependent: set(para_into).
% 1.63/1.85 dependent: clear(para_from_right).
% 1.63/1.85 dependent: clear(para_into_right).
% 1.63/1.85 dependent: set(para_from_vars).
% 1.63/1.85 dependent: set(eq_units_both_ways).
% 1.63/1.85 dependent: set(dynamic_demod_all).
% 1.63/1.85 dependent: set(dynamic_demod).
% 1.63/1.85 dependent: set(order_eq).
% 1.63/1.85 dependent: set(back_demod).
% 1.63/1.85 dependent: set(lrpo).
% 1.63/1.85 dependent: set(hyper_res).
% 1.63/1.85 dependent: set(unit_deletion).
% 1.63/1.85 dependent: set(factor).
% 1.63/1.85
% 1.63/1.85 ------------> process usable:
% 1.63/1.85 ** KEPT (pick-wt=5): 1 [] -r1(A)|A=$c1.
% 1.63/1.85 ** KEPT (pick-wt=5): 2 [] A!=$c1|r1(A).
% 1.63/1.85 ** KEPT (pick-wt=7): 3 [] -r2(A,B)|B=$f1(A).
% 1.63/1.85 ** KEPT (pick-wt=7): 4 [] A!=$f1(B)|r2(B,A).
% 1.63/1.85 ** KEPT (pick-wt=9): 5 [] -r3(A,B,C)|C=$f2(A,B).
% 1.63/1.85 ** KEPT (pick-wt=9): 6 [] A!=$f2(B,C)|r3(B,C,A).
% 1.63/1.85 ** KEPT (pick-wt=9): 7 [] -r4(A,B,C)|C=$f3(A,B).
% 1.63/1.85 ** KEPT (pick-wt=9): 8 [] A!=$f3(B,C)|r4(B,C,A).
% 1.63/1.85 ** KEPT (pick-wt=12): 9 [] -r2(A,B)|B!=C| -r2(D,C)|A=D.
% 1.63/1.85 ** KEPT (pick-wt=8): 10 [] -r1(A)|A!=B| -r2(C,B).
% 1.63/1.85 ** KEPT (pick-wt=18): 11 [] -r3(A,B,C)|C!=D| -r2(E,D)| -r2(F,E)| -r1(G)| -r2(G,F).
% 1.63/1.85
% 1.63/1.85 ------------> process sos:
% 1.63/1.85 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.63/1.85 ** KEPT (pick-wt=5): 18 [] r2(A,$f4(B,A)).
% 1.63/1.85 ** KEPT (pick-wt=8): 19 [] r3(A,$f4(A,B),$f5(A,B)).
% 1.63/1.85 ** KEPT (pick-wt=7): 21 [copy,20,flip.1] $f7(A,B)=$f5(A,B).
% 1.63/1.85 ---> New Demodulator: 22 [new_demod,21] $f7(A,B)=$f5(A,B).
% 1.63/1.85 ** KEPT (pick-wt=7): 24 [copy,23,demod,22] r2($f6(A,B),$f5(A,B)).
% 1.63/1.85 ** KEPT (pick-wt=6): 25 [] r3(A,B,$f6(A,B)).
% 1.63/1.85 ** KEPT (pick-wt=5): 26 [] r2(A,$f8(B,A)).
% 1.63/1.85 ** KEPT (pick-wt=8): 27 [] r4(A,$f8(A,B),$f9(A,B)).
% 1.63/1.85 ** KEPT (pick-wt=7): 28 [] $f9(A,B)=$f11(A,B).
% 1.63/1.85 ---> New Demodulator: 29 [new_demod,28] $f9(A,B)=$f11(A,B).
% 1.63/1.85 ** KEPT (pick-wt=8): 30 [] r3($f10(A,B),A,$f11(A,B)).
% 1.63/1.85 ** KEPT (pick-wt=6): 31 [] r4(A,B,$f10(A,B)).
% 1.63/1.85 ** KEPT (pick-wt=3): 32 [] r1($f12(A)).
% 1.63/1.85 ** KEPT (pick-wt=6): 33 [] r3(A,$f12(A),$f13(A)).
% 1.63/1.85 ** KEPT (pick-wt=4): 34 [] $f13(A)=A.
% 1.63/1.85 ---> New Demodulator: 35 [new_demod,34] $f13(A)=A.
% 1.63/1.85 ** KEPT (pick-wt=3): 36 [] r1($f14(A)).
% 1.63/1.85 ** KEPT (pick-wt=6): 37 [] r4(A,$f14(A),$f16(A)).
% 1.63/1.85 ** KEPT (pick-wt=3): 38 [] r1($f15(A)).
% 1.63/1.85 ** KEPT (pick-wt=5): 39 [] $f16(A)=$f15(A).
% 1.63/1.85 ---> New Demodulator: 40 [new_demod,39] $f16(A)=$f15(A).
% 1.63/1.85 ** KEPT (pick-wt=8): 41 [] r1($f17(A))|r2($f19(A),$f18(A)).
% 1.63/1.85 ** KEPT (pick-wt=7): 43 [copy,42,flip.2] r1($f17(A))|$f18(A)=A.
% 1.63/1.85 ** KEPT (pick-wt=9): 45 [copy,44,flip.1] $f17(A)=A|r2($f19(A),$f18(A)).
% 1.63/1.85 ** KEPT (pick-wt=8): 47 [copy,46,flip.1,flip.2] $f17(A)=A|$f18(A)=A.
% 1.63/1.85 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.63/1.85 17 back subsumes 12.
% 1.63/1.85 >>>> Starting back demodulation with 22.
% 1.63/1.85 >>>> Starting back demodulation with 29.
% 1.63/1.85 >> back demodulating 27 with 29.
% 1.63/1.85 >>>> Starting back demodulation with 35.
% 1.63/1.85 >> back demodulating 33 with 35.
% 1.63/1.85 >>>> Starting back demodulation with 40.
% 1.63/1.85 >> back demodulating 37 with 40.
% 1.63/1.85
% 1.63/1.85 ======= end of input processing =======
% 1.63/1.85
% 1.63/1.85 =========== start of search ===========
% 1.63/1.85
% 1.63/1.85 -------- PROOF --------
% 1.63/1.85
% 1.63/1.85 -----> EMPTY CLAUSE at 0.00 sec ----> 87 [hyper,61,11,34,53,53,54,53] $F.
% 1.63/1.85
% 1.63/1.85 Length of proof is 5. Level of proof is 2.
% 1.63/1.85
% 1.63/1.85 ---------------- PROOF ----------------
% 1.63/1.85 % SZS status Theorem
% 1.63/1.85 % SZS output start Refutation
% See solution above
% 1.63/1.85 ------------ end of proof -------------
% 1.63/1.85
% 1.63/1.85
% 1.63/1.85 Search stopped by max_proofs option.
% 1.63/1.85
% 1.63/1.85
% 1.63/1.85 Search stopped by max_proofs option.
% 1.63/1.85
% 1.63/1.85 ============ end of search ============
% 1.63/1.85
% 1.63/1.85 -------------- statistics -------------
% 1.63/1.85 clauses given 10
% 1.63/1.85 clauses generated 60
% 1.63/1.85 clauses kept 73
% 1.63/1.85 clauses forward subsumed 32
% 1.63/1.85 clauses back subsumed 1
% 1.63/1.85 Kbytes malloced 976
% 1.63/1.85
% 1.63/1.85 ----------- times (seconds) -----------
% 1.63/1.85 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.85 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.85 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.63/1.85
% 1.63/1.85 That finishes the proof of the theorem.
% 1.63/1.85
% 1.63/1.85 Process 9205 finished Wed Jul 27 02:41:26 2022
% 1.63/1.85 Otter interrupted
% 1.63/1.85 PROOF FOUND
%------------------------------------------------------------------------------